In a semiconductor manufacturing process, various kinds of semiconductor manufacturing apparatuses or semiconductor inspection apparatuses may be employed. For example, a plasma processing apparatus is used for a plasma processing such as an etching process or a film forming process. These kinds of plasma processing apparatus include an upper electrode and a lower electrode, which are arranged to be parallel with each other in a processing chamber. If a high frequency power is applied to the lower electrode and a processing gas is introduced into the processing chamber, a plasma of the processing gas is generated by discharging between the upper and lower electrodes. As a result, a predetermined plasma processing is performed on an object to be processed (e.g., a wafer).
For evaluating whether or not an abnormality exists in the process of the plasma processing apparatus, 30 or so kinds of data are detected with use of respective detectors, wherein the detected data include a plasma emission intensity, a pressure in the processing chamber, a power applied to the lower electrode, a supplying flow rate of the processing gas, and etc. The respective detected values are collected as operating data, which are used to perform a multivariate analysis such as principal component analysis. Accordingly, the process of the plasma processing apparatus is evaluated.
For example, after processing multiple wafers, a plurality of operating data is obtained for each of the wafers. For example, a graph shown in FIG. 12 can be obtained by, e.g., gathering 3 kinds of operating data for each of the wafers and plotting the operating data. In the graph shown in FIG. 12, the operating data show a regular trend, namely, most of the operating data are enclosed in a Rugby-ball-shaped space. Thus, if a principal component analysis is performed on the operating data to obtain first and second principal components, the first principal component becomes the line coordinate {circle around (1)} which has the largest variance and is approximately identical to the major axis of the Rugby-ball-shaped space, while the second principal component becomes the line coordinate {circle around (2)} which has second largest variance and is approximately identical to the minor axis of the Rugby-ball-shaped space. The line coordinate {circle around (1)} and the line coordinate {circle around (2)} are orthogonal to each other. Then, the process of the plasma processing apparatus etc. is evaluated by using, e.g., the first principal component.
However, as can be seen clearly in FIG. 12, there are operating data that are outside the Rugby-ball-shaped space such as points A and B, for example. These operating data are considered to be outside the normal operating data. Thus, some abnormality is considered to exist in the plasma processing apparatus.
As a method for investigating the cause of such abnormality, the applicants have proposed a method for investigating the cause of an abnormality of a plasma processing apparatus by using a residual matrix in a principal component analysis in Japanese Patent Laid-Open Application No. 2002-25981. In the method, values, which are detected by multiple detectors while processing multiple sample wafers, are employed as operating data, and a model equation is constructed by performing a principal component analysis on the operating data. Then, principal components with high degrees are merged to obtain a residual matrix, whose components (residuals) are used to inspect the abnormality of the plasma processing apparatus. Further, by obtaining a sum of squares of respective components of the residual matrix (a residual score), the abnormality of the plasma processing apparatus can be recognized by using a magnitude of difference between a base line (average level line) of residual scores for respective wafers in a case where a standardized processing apparatus is employed, and a base line of residual scores in a case where another plasma processing apparatus is employed.
However, the abnormality inspection method of Japanese Patent Laid-Open Application No. 2002-25981 is problematic when operating data are collected by processing multiple training wafers by using a processing apparatus after a maintenance procedure such as cleaning, and then the operating data are applied, in order to obtain a residual score, to the principal component analysis model equation, which is obtained by using the processing apparatus before cleaning. In that case, as shown in FIG. 13, even if the processing apparatus after the cleaning is in a normal status, the base line {circle around (2)}, which is formed by residual scores for respective wafers after the maintenance, migrates from the base line {circle around (1)}, which is formed by residual scores for respective wafers before the maintenance, to exceed the abnormality determination line L, thereby determining that the process of the processing apparatus is abnormal. As such, an abnormality cannot be properly checked for every wafer in such a case. Further, it is recognized that as the maintenance such as cleaning is repeated, the base lines {circle around (3)} and {circle around (4)} slowly shift upward from the base line {circle around (2)} and the abnormality becomes unidentifiable. In this case, the graph shown in FIG. 13 is obtained as follows: first, plasma emission intensities in multiple component wavelengths within a predetermined range of wavelength are employed as operating data, wherein the plasma emission intensities are detected by an endpoint detector; then an average of residual scores, of the emission intensities in all component wavelengths, is calculated for each of the wafers; and finally the average of the residual scores is plotted for each of the wafers.
Further, in a semiconductor manufacturing process, many kinds of semiconductor manufacturing apparatuses or semiconductor inspection apparatuses may be employed. For example, a plasma processing apparatus is used for a plasma processing such as etching or film forming processes. These kinds of plasma processing apparatus include an upper electrode and a lower electrode, which are arranged to be parallel with each other in a processing chamber. If high frequency powers are applied to the upper and lower electrodes under the control of a control device and a processing gas is introduced into the processing chamber, a plasma of the processing gas is generated by a discharge between the upper and lower electrodes. While emission intensities of the plasma are monitored by using an endpoint detector, a predetermined plasma processing is performed on an object to be processed (e.g., a wafer). Here, controllable parameters, such as a pressure in the processing chamber, high frequency powers for the upper and lower electrodes, a flow rate of the processing gas, and etc., (hereinafter, referred to as “process parameters”) are set to be a standard condition. While processing the wafer, plasma emission intensities etc. are detected with a plurality of detectors, such as an endpoint detector etc., which are attached to the plasma processing apparatus.
Thereafter, a model equation for predicting the process is constructed based on multiple detected data with a multivariate analysis program that is stored in the control device. With the model equation, a status of the plasma processing apparatus is evaluated or a processing result is predicted. For constructing the model equation, detected data from a plurality of detectors are collected, and a correlation equation between the detected data and the process parameters is obtained by a multiple regression analysis. By applying detected data to the model equation constructed by the multiple regression analysis, process parameters can be predicted.
For constructing the model equation, first of all, a predetermined number of wafers, e.g., 7 wafers, are arranged in the processing chamber of the plasma processing apparatus. Then, the wafers are processed under the process parameters, such as the pressure in the processing chamber, the high frequency powers for the upper and lower electrodes, the flow rate of the processing gas, and etc., being set to be at a standard condition (normal condition which has been set previously depending on the processing details). While processing the wafers, plasma emission intensities (optical data) in multiple component wavelengths are detected by an endpoint detector as detected data. The wafers processed in the standard condition are defined as normal wafers.
Thereafter, for example, 12 wafers are processed after changing multiple process parameters within a predetermined range from the standard condition. Then, multiple optical data are detected as detected data for each of the wafers. In varying (changing) the process parameters, an orthogonal experiment employing orthogonal arrays of Taguchi method is performed. The wafers used for the orthogonal experiment are defined as orthogonal arrays wafers.
Using the detected data from the normal wafers and the orthogonal arrays wafers, a multiple regression analysis, such as shown in FIG. 15, is performed. That is, the following model equation is constructed by performing a multiple regression analysis by using the multiple detected data including the optical data as explanatory variables xij (i being the wafer number, j being the sample number of the component wavelengths) and the process parameters, such as the pressure of the processing gas in the processing chamber, the high frequency powers and the flow rate of the processing gas, as objective variables yij. For constructing the model equation, the partial least squares (PLS) method, which can be used to obtain the correlation between the matrices X and Y with only a few data, is employed to obtain the matrix B. The details of the PLS method is published in, e.g., JOURNAL OF CHEMOMETRICS, VOL. 2(PP. 211-228) (1998). Further, in the following model equation, X is a matrix whose components include explanatory variables, B is a matrix whose components include multiple regression coefficients, and Y is a matrix whose components include objective variables.Y=BX
After the model equation is constructed, normal wafers and abnormal wafers (wafers that are processed in a changed condition wherein the process parameters are varied in a upward or downward direction from the standard condition) are processed, and the process parameters are predicted with use of data detected while processing the wafers. That is, 7 wafers are processed as normal wafers in the process parameters set to be the standard condition, while 15 wafers are processed as abnormal wafers in a condition wherein the process parameters are varied in a upward or downward direction from the standard condition. Meanwhile, plasma emission intensities in multiple component wavelengths are detected by an endpoint detector as detected data. Then, the multiple process parameters are calculated based on the model equation and the detected data, and the calculated values are automatically outputted as predicted values.
FIG. 16 shows a comparison between set values and predicted values of a process parameter for respective wafers before and after a cleaning procedure. The left half of FIG. 16 shows set values and predicted values of a flow rate of gas 1 in case of the plasma processing apparatus before the cleaning, where the model equation is constructed. The right half of FIG. 16 shows set values and predicted values (with use of the model equation) of the flow rate of the gas 1 in case of the plasma processing apparatus after the cleaning. As can be clearly seen in FIG. 16, when the plasma processing apparatus before the cleaning where the model equation is constructed, the predicted values are near to the setting values, that is, the prediction accuracy is relatively high.
However, as for the plasma processing apparatus after the cleaning, the predicted values diverge away from the setting values. That is, if the model equation constructed before the cleaning is used intact, the process parameters for the plasma processing apparatus after the cleaning cannot be predicted. Even with a single plasma processing apparatus, detected data would change after a cleaning due to re-attachment of an endpoint detector, environmental changes in a processing chamber, and etc. Therefore, it is necessary that the model equation should be reconstructed after the cleaning. The above is not limited to a single plasma processing apparatus before and after cleaning, but is similar when another maintenance procedure and between separate plasma processing apparatuses of same kind.